2831
The Journal of Experimental Biology 206, 2831-2843
© 2003 The Company of Biologists Ltd
doi:10.1242/jeb.00481
Comparative studies of high performance swimming in sharks
I. Red muscle morphometrics, vascularization and ultrastructure
D. Bernal1,*, C. Sepulveda1, O. Mathieu-Costello2 and J. B. Graham1
1Center for Marine Biotechnology and Biomedicine and Marine Biology Research Division, Scripps Institution of
Oceanography, University of California San Diego, La Jolla, CA 92093-0204, USA and 2Department of Medicine,
University of California San Diego, La Jolla, CA 92093-0623, USA
*Author for correspondence at present address: Department of Zoology, Weber State University, Ogden, UT 84408-2505, USA
(e-mail: [email protected])
Accepted 8 May 2003
Summary
Tunas (family Scombridae) and sharks in the family
occupies the position where it is typically found in most
Lamnidae are highly convergent for features commonly
fishes; more posterior and along the lateral edge of the
related to efficient and high-performance (i.e. sustained,
body. Comparisons among sharks in this study revealed
aerobic) swimming. High-performance swimming by
no differences in the total RM quantity (approximately
2–3% of body mass) and, irrespective of position within
fishes requires adaptations augmenting the delivery,
the body, RM scaling is isometric in all species. Sharks
transfer and utilization of O2 by the red myotomal muscle
thus have less RM than do tunas (4–13% of body mass).
(RM), which powers continuous swimming. Tuna
Relative to published data on other shark species, mako
swimming performance is enhanced by a unique anterior
and centrally positioned RM (i.e. closer to the vertebral
RM appears to have a higher capillary density, a greater
column) and by structural features (relatively small fiber
capillary-to-fiber ratio and a higher myoglobin
concentration. However, mako RM fiber size does not
diameter, high capillary density and greater myoglobin
differ from that reported for other shark species and the
concentration) increasing O2 flux from RM capillaries to
total volume of mitochondria in mako RM is similar to
the mitochondria. A study of the structural and
that reported for other sharks and for tunas. Lamnid RM
biochemical features of the mako shark (Isurus
oxyrinchus) RM was undertaken to enable performanceproperties thus suggest a higher O2 flux capacity than in
capacity comparisons of tuna and lamnid RM. Similar to
other sharks; however, lamnid RM aerobic capacity
tunas, mako RM is positioned centrally and more anterior
appears to be less than that of tuna RM.
in the body. Another lamnid, the salmon shark (Lamna
ditropis), also has this RM distribution, as does the closely
Key words: lamnid shark, tuna, myotome, red muscle, aerobic
capacity, myoglobin, muscle ultrastructure, scaling, allometry,
related common thresher shark (Alopias vulpinus; family
Lamnidae, Scombridae, Isurus, Lamna, Alopias, Mustelus, Triakis,
Alopiidae). However, in both the leopard shark (Triakis
Prionace.
semifasciata) and the blue shark (Prionace glauca), RM
Introduction
A marked evolutionary convergence has been demonstrated
for the lamnid sharks (order Lamniformes; family Lamnidae)
and tunas (order Perciformes; family Scombridae) in
specializations related to an increased capacity for sustained,
aerobic locomotion (i.e. high-performance swimming; Bernal
et al., 2001a). The sustained swimming of all fishes is powered
by the red myotomal muscle (RM; Bone, 1978a) and, in most
species, RM occurs along the posterior lateral edges of the
body and is the dominant fiber type in that region
[approximately 75–85% fork length (FL)] subject to maximal
body bending during caudal thrust production (Greer-Walker
and Pull, 1975). Lamnids and tunas, however, are different in
having their RM in a more anterior and central position
(Graham et al., 1983; Carey et al., 1985; Graham and Dickson,
2000, 2001; Bernal et al., 2001a).
The ‘high-performance swimming adaptations’ of tunas and
lamnids include features enhancing tissue O2 transfer at the
gills (i.e. a large gill-surface area), the capacity to deliver a
large quantity of O2 to the RM (i.e. a large heart with a thick
compact myocardial layer, a large stroke volume and welldeveloped coronary circulation and both a high blood
hemoglobin concentration [Hb] and hematocrit) and regional
endothermy (Dickson, 1996; Lai et al., 1997; Bernal et al.,
2001a; Brill and Bushnell, 2001; Korsmeyer and Dewar,
2001). Although the presence of these high-performance
adaptations in tunas and lamnids suggests that both groups are
capable of sustaining a higher aerobic metabolism during
swimming relative to that of other fishes (Bernal et al., 2001a),
there is no direct experimental evidence that these adaptations
increase swimming efficiency (Katz, 2002).
2832 D. Bernal and others
Relative to the RM of other fishes, tuna RM receives a large
percentage of cardiac output (White et al., 1988) and has a
greater capacity for mitochondrial oxidative phosphorylation
(i.e. ATP production; Dickson, 1995, 1996). Consistent with
the heightened aerobic capacity of tuna RM are structural and
biochemical features favoring O2 transfer from the RM
capillaries to the fiber mitochondria. These include a relatively
small RM fiber diameter, high capillary densities, the presence
of capillary manifolds, which increase capillary surface area to
fiber volume ratio, and a higher muscle myoglobin
concentration [Mb], which enhances the diffusion of O2 from
the blood into the muscle cells (Wittenberg, 1970; Bone,
1978b; Mathieu-Costello et al., 1992, 1995, 1996; Dickson,
1995, 1996; Sidell, 1998; Suzuki and Imai, 1998).
The objective of this study is to provide comparative data
on the position and quantity of lamnid RM and on this tissue’s
structural properties related to high-performance swimming.
Although lamnid sharks are thought to have RM
specializations for enhanced O2 transfer that are comparable to
those of tunas, this has not been documented. Also, data
showing the position of the maximal RM cross-sectional area
of makos and other lamnids presented by Carey et al. (1985)
are suggestive of a tuna-like RM distribution pattern but
indicate a much smaller RM quantity in lamnids relative to
tunas. Using mako sharks and other lamnids, we have
quantified RM position and developed an algorithm to extract
more quantitative RM data from the findings of Carey et al.
(1985). We also report preliminary RM ultrastructural and
biochemical findings relating to lamnid RM aerobic capacity
and compare these features with those of other non-lamnid
sharks and tunas.
Materials and methods
Specimens used in this study were captured, maintained and
euthanized following procedures dictated by the type of study
(described below) and in accordance with protocols approved
by the University of California San Diego Institutional Animal
Care and Use Committee.
RM distribution and quantification
The longitudinal distribution of RM was measured in two
lamnid and three non-lamnid shark species. The lamnid sharks
are the shortfin mako shark (Isurus oxyrinchus Rafinesque
1810; body mass, 5–50·kg; N=8) and the salmon shark (Lamna
ditropis Hubbs and Follet 1947; 15.9–148·kg; N=2). The three
non-lamnid sharks are the common thresher shark (Alopias
vulpinus Bonnaterre 1788; 9.1–70.4·kg; N=6) and two species
in the order Carcharhiniformes, the blue shark (Prionace
glauca L.; family Carcharhinidae; 2.1–22.2·kg; N=4) and the
leopard shark (Triakis semifasciata Girard 1855; family
Triakidae; 1.4–15·kg; N=3).
In all of the species studied, measurable quantities of RM
did not occur anterior to 23–25% FL. Beginning at this
position, whole frozen sharks were cut into approximately
2–3·cm-thick transverse sections to the caudal peduncle
(85–95% FL). In the common thresher shark, where the RM
extends far into the very long upper caudal fin lobe (Fig.·1),
sections were extended to 140% FL.
High-resolution digital images of the anterior side of each
section were obtained and the cross-sectional area of RM
determined (NIH Image 4.02). For all sharks, the longitudinal
distribution of RM was obtained by transforming the RM
surface area (cm2) at 50% FL (see Table·1) to a relative
value of 1 and using this value as the reference point for all
other positions along the body. The volume of RM in each
slice was calculated as the product of the RM surface area
(mean of the anterior and posterior faces of each slice) and
slice thickness. Red muscle mass in each slice was
determined as the product of RM volume and RM density
(predetermined to be 1.05±0.02·g·cm–3, mean ± S.E.M.;
N=10), with the sum of RM in all sections indicating total
RM mass (TRMM) for the shark. Our image analysis (IA)
TRMM methodology was validated for three makos (5.3·kg,
14.0·kg and 16.6·kg) by comparing TRMM results from IA
with values obtained by gross dissection and gravimetric
determination (GD).
The TRMM and RM linear distribution determinations for
mako sharks in this study enabled us to convert the RM data
presented by Carey et al. (1985) into additional estimates of
TRMM. These workers had originally reported the maximal
RM cross-sectional area of nine makos (5–75·kg) and
expressed TRMM as a percentage of total axial muscle mass.
By combining the RM data for seven of those makos with our
mako RM distribution analysis, we were able to express them
in terms of percentage body mass.
Myoglobin analysis
General
Red muscle myoglobin concentration [Mb] was quantified
using a modification of the high-performance liquid
chromatography (HPLC) method of Kryvi et al. (1981). Fresh
or frozen (–80°C) RM samples were obtained from I.
oxyrinchus (5.9–46.7·kg; N=10), L. ditropis (91.2–114·kg;
N=2) and A. vulpinus (6.35–45.5·kg; N=7). To compare our
methods with those of Kryvi et al. (1981), we measured the
RM [Mb] in one specimen of the gray smoothhound (Mustelus
californicus; order Carcharhiniformes; family Triakidae;
0.8·kg), which belongs to the same order and has an RM
distribution pattern similar to that of the species studied by
those investigators.
Approximately 0.2·g of RM was homogenized in a 15·ml
tissue grinder (Kontes Duall 23) using 9× the tissue mass of
running buffer (30·mmol·l–1 KH2PO4, pH 7.2 at 20°C). Solid
particulates were separated by centrifugation at 12·000·g for
10·min at 4°C and the supernatant containing the dissolved Mb
was removed and diluted 2× using running buffer. Sufficient
Na2S2O4 (approximately 1·mg) was added to each sample
supernatant to ensure that Mb was in the reduced state (cherry
red in color) prior to passing the sample through a 0.45·µm
syringe filter (Gelman Acrodisc LC 13 PVDF).
Red muscle characteristics in sharks 2833
HPLC parameters
Separation of tissue Mb and Hb is based on their different
molecular masses (Mb, ~16·kDa; Hb, ~64·kDa) and thus their
different elution times through a silica-based size exclusion
column [Alltech PEEK Macrosphere GPC (60·Å; 7·µm;
4.6·mm diameter × 250·mm length), protected by a guard
column (Alltech MF Guard; 60 Å; 6·µm)]. The gel permeation
column (approximately 1.7·ml exclusion volume) was
equilibrated with at least 150·ml of running buffer prior to the
injection of the first sample. A 200·µl injection loop was used
to load 25·µl of filtered and reduced tissue homogenates.
Myoglobin was quantified by flowing degassed running buffer
(0.3·ml·min–1) through a diode array detector (Beckman Gold
168) at 413·nm.
Myoglobin quantification
A linear relationship (r=0.99) between known quantities of
purified Mb (Sigma M 0630) and the integrated area
under the curve was used to quantify RM [Mb]. The
lower [Mb] detection limit was 17·pmol Mb
(0.28·mg·Mb·g–1·tissue·wet·mass). Verification of an adequate
size-based separation was established by the injection of mixed
Mb and Hb (Sigma H 4632) standards and the resulting timeseparated maximum absorbance peaks.
RM vascularization and ultrastructure
The tissues of two mako sharks (95·cm FL, 9·kg; 100·cm
FL, 12·kg) were fixed in situ via perfusion of glutaraldehyde
following methods detailed in Mathieu-Costello et al. (1992).
Sharks were attracted to the boat, dip netted and returned to
the laboratory alive (see Bernal et al., 2001b). Once in the
laboratory, sharks were secured ventral-side up in a restraining
V-board, and a 2.5·cm-diameter hose was inserted into the
mouth to ensure that well-oxygenated running seawater flowed
over the gills during the entire procedure. A dose of anesthetic
(1:5000; MS-222) was mixed with seawater and the fish was
ventilated for an additional 5–10·min to allow for complete
sedation before surgery.
A midline incision exposed the heart, and a cannula was
inserted into the conus arteriosus. All systemic blood returning
to the heart was drained by cutting away the sinus venosus.
Perfusion with heparinized saline solution [574·mmol·l–1 NaCl
(approximately 1100·mosmol·l–1) containing 20·ml·l–1
1000·sodium heparin USP; Elkins-Sinn Inc., Cherry Hill, NJ,
USA] preceded the fixative solution [6.25% glutaraldehyde in
0.1·mol·l–1 sodium cacodylate (Polysciences Inc., Warrington,
PA, USA) buffer, pH 7.4 at 20°C, 132·mmol·l–1 NaCl
(approximately 1100·mosmol·l–1)]. Both the saline solution and
the fixative buffer were administered at an in vivo non-pulsatile
blood pressure of approximately 9.3 kPa (Lai et al., 1997).
Following perfusion, RM samples (1·cm×4·mm×1·mm;
approximately 0.04·g) were taken at approximately 45% FL
(under the first dorsal fin) and cut into longitudinal strips for
storage in the fixative solution. Samples were minced into
small blocks (1·mm×1·mm×2·mm) for subsequent transverse
(α=0°, angle between normal section and muscle fiber axis)
and longitudinal (α=π/2) section orientations and postfixed
with osmium tetroxide solution prior to being embedded in
Araldite for morphometric analyses using light microscopy and
transmission electron microscopy, as described in MathieuCostello et al. (1992).
Sections (1·µm) from each mako shark were cut in
transverse (4–6 blocks per shark) and longitudinal (2 blocks)
orientations and stained with 0.1% aqueous Toluidine Blue
solution. Morphometric analyses followed the methods in
Mathieu-Costello et al. (1992) for tuna locomotor muscle. The
mean sarcomere length (lo) in each mako was estimated from
longitudinal sections by direct measurements of 40 muscle
cells at 1000× magnification. A section angle closest to π/2 was
determined by rotating the tissue block on the microtome in 1°
increments until the shortest lo was measured in the sections.
Mean fiber cross-sectional area [ā(f)], and capillary density per
mm2 sectional area of muscle fiber [transverse, QA(0);
longitudinal, QA(π/2)] were estimated by point-counting, at
400× magnification, one transverse section from each block
(total 10 blocks). Capillary density was calculated from the
longitudinal sections (2 blocks) in the 9·kg mako but not in the
12·kg specimen because the capillaries were partially collapsed
as a result of an incomplete perfusion fixation.
The ratio QA(0)/QA(π/2) was used to calculate the capillary
anisotropy concentration parameter, K (from tables in Mathieu
et al., 1983), and then to estimate the orientation coefficient
c(K,0), which relates the capillary counts per unit area of fiber
in a transverse orientation and is used to estimate the relative
increase in capillary length per volume of muscle fiber. A
c(K,0) of 1 indicates that capillaries run straight and parallel
to the muscle fiber axis and are unbranched, while the
maximum c(K,0) value of 2 indicates that there is no
preferential orientation relative to the muscle fiber axis (i.e. it
is random; Mathieu et al., 1983). The product of QA(0) and
c(K,0) was used to estimate total capillary length per volume
of muscle fiber, JV(c,f) [i.e. this term includes the contributions
of capillary tortuosity (vessel convolutions that increase the
fiber contact area) and branching; Mathieu-Costello et al.,
1992]. The mean number of capillaries surrounding each
muscle fiber (NCAF) were estimated by counting directly at a
magnification of 400× (n=≥200 fibers per muscle sample), and
the mean fiber diameter [d̄(f)] was estimated by 2·[ā(f)/π]0.5,
assuming a circular fiber cross-sectional area. Mean capillary
diameter [d̄(c)] was measured (n=21) using a 1·µm scale
eyepiece grid at a magnification of 400×. Measurement of d̄(c)
was limited to circle-shaped capillary sections in which the
ratio between the smaller and larger diameters did not exceed
1.2 (i.e. 20%).
Mitochondrial density was measured using a total of eight
tissue blocks (four from each mako) from which ultrathin
(50–70·nm) transverse sections were obtained and contrasted
with uranyl acetate and bismuth subnitrate (Mathieu-Costello
et al., 1992). The volume densities of mitochondria and
myofibrils were each measured by point-counting on 70·mm
film micrographs (30–38 for each muscle sample) taken by
2834 D. Bernal and others
systematic random sampling of one transverse section from
each block examined at a final magnification of 9208× using a
Zeiss 10 transmission electron microscope (Mathieu-Costello
et al., 1992).
Student’s t-test was used to determine if b=1 (i.e. isometric
scaling). The mean values for different data sets were
compared using a Student’s t-test.
Statistical analysis
All statistical analyses were performed at a significance level
of α=0.05. The allometric relationship aMb±95%C.I. (where a is
a constant and M is body mass) was used to obtain the scaling
coefficient b for TRMM in the different shark species, and a
Results
RM distribution
The linear distributions of RM in the five shark species are
shown in Fig.·1. Table·1 contains the corresponding
morphological data for each shark studied and data for other
1.4
1.4
A
1.2
1.2
1.0
1.0
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
10 20 30 40 50 60 70 80 90 100 110 120
Relative red muscle cross-sectional area
0 10 20 30 40 50 60 70 80 90 100 110 120
1.4
B
1.4
1.2
1.2
1.0
1.0
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0 10 20 30 40 50 60 70 80 90 100 110 120
1.4
C
D
10 20 30 40 50 60 70 80 90 100 110 120
E
1.2
1.0
0.8
0.6
0.4
0.2
0 10 20 30 40 50 60 70 80 90 100 110 120
% Fork length
Fig.·1. Red muscle (RM) distribution patterns in five shark species. Sharks having a more posterior and lateral RM position are (A) blue shark
(Prionace glauca) and (B) leopard shark (Triakis semifasciata). Sharks that have a more anterior and central RM position are (C) salmon shark
(Lamna ditropis), (D) shortfin mako (Isurus oxyrinchus) and (E) common thresher shark (Alopias vulpinus). The relative amounts of RM in the
different positions along the body are expressed as a proportion of the RM cross-sectional area equal to 1 at 50% fork length (see Table·1 for
maximum surface area in cm2). Values are means ± S.E.M., except in L. ditropis, where values are means ± range. Half transverse sections of
sharks showing the position of the RM (RM digitally enhanced for clarity); broken lines indicate the fork length position of the transverse
section. Shark illustrations modified from Goodson (1988), Last and Stevens (1994), Allen (1997) and Tricas et al. (1997), used with permission.
Red muscle characteristics in sharks 2835
Table 1. Shark red muscle (RM) body position, quantities and allometry based on data from the present study and Carey
et al. (1985)
Species
(common name)
RM
position
Ref.
Prionace glauca
(blue shark)
PL
a
Body
mass
(kg)
Fork
length
(cm)
2.1
12.0
18.6
22.2
69
123
141
150
N
RM cross-sectional
area at 50%
FL (cm2)
0.69
5.46
8.82
8.81
4
Triakis semifasciata
(leopard shark)
PL
a
1.34
1.44
15.0
52
65
118
0.66
0.75
5.12
3
Isurus paucus
(longfin mako)
Isurus oxyrinchus
(shortfin mako)
AC
b
–
–
AC
a
5.3
8.6
14.0
14.3
16.6
20.6
25.8
49.9
77
89
110
113
115
125
138
164
–
–
3.19
6.71
7.26
10.06
10.05
9.55
11.42
18.42
8
b
5
19
25
33
52
53
75
80†
123†
134†
146†
169†
170†
189†
4.28
10.83
15.90
14.83
18.20
17.03
22.52
7
Carcharodon carcharias
(white shark)
AC
b
23.6
227
297
1256
115§
235§
256§
405§
Lamna ditropis
(salmon shark)
AC
a
15.9
148
105
201
6.8
54.2
88.3
267.0
RM mass
(% of body mass)
1.05
2.70
3.52
3.31
Mean ± S.E.M.
2.65±0.56
1.72
2.38
2.09
Mean ± S.E.M.
2.06±0.19
~2
1.80
1.88
1.85
2.32
2.14
2.10
1.79
2.20
Mean ± S.E.M.
2.01±0.07
2.14‡
2.19‡
2.67‡
2.06‡
1.86‡
1.72‡
1.79‡
Mean ± S.E.M.
2.06±0.12
~3
~3
~3
~6
4
12.91
36.53
2
Lamna nasus
(porbeagle shark)
Alopias vulpinus
(common thresher)
AC
b
–
–
AC
a
4.5
20.9
24.9
34.9
37.2
70.4
85
105
120
124
123
163
1
–
5.61
8.82
13.40
12.91
15.31
35.13
6
2.38
1.80
Mean (range)
2.09 (1.8–2.4)
~2
2.02
1.98
2.83
1.96
2.11
3.14
Mean ± S.E.M.
2.34±0.21
Abbreviations: a, present study; b, Carey et al. (1985); AC, anterior and central; PL, posterior and lateral.
*Scaling equation: aMb±95%C.I, where a is a constant, M is mass (kg) and b is the scaling coefficient.
†Fork length estimated from Kohler et al. (1994).
‡Red muscle mass values estimated by using the RM longitudinal distribution analysis in Fig.·1.
§Fork length estimated from Mollet and Cailliet (1996).
RM scaling*
0.007M1.51±0.18
r2=0.99
0.020M1.02±1.51
r2=0.99
0.017M1.07±0.13
r2=0.98
0.027M0.91±0.16
r2=0.98
0.016M1.15±0.44
r2=0.98
0.034M0.88
–
0.013M1.16±0.35
r2=0.96
2836 D. Bernal and others
RM scaling
The image analysis (IA) and gravimetric (GD) techniques
for TRMM determination are in good agreement. Respective
values for the three makos studied are given in terms of body
mass (kg) and TRMM (kg) for IA/GD techniques: 5.3,
0.099/0.095; 14.0, 0.255/0.260; 16.6, 0.337/0.355. Table·1
shows the TRMM determined for each shark studied and also
includes values for seven of the makos for which TRRM mass
was estimated from the maximum RM cross-sectional area data
reported by Carey et al. (1985). There is no significant
difference in the RM scaling coefficients for the shark species
studied and there is considerable overlap in the percentage of
RM found for all species (Table·1). Moreover, the scaling
coefficients and the relative amount of RM are not different,
even when the shark species are separated into two distinct
groups based on similarities in RM position [i.e. in a more
posterior and lateral position (blue sharks and leopard sharks)
vs a more anterior and central position (mako sharks, salmon
sharks and common thresher sharks); Table·1]. Thus, the entire
RM data set for the five species was combined to form a single
scaling function (0.018M1.05±0.08; r2=0.96, N=30; Fig.·2). This
function adequately describes RM scaling in all of the sharks
studied, irrespective of the marked differences in RM position
documented in Fig.·1. The scaling coefficient in this equation
is not different from 1.0 (indicating isometric RM scaling) and
there is no significant difference (one-way ANOVA, P≤0.05)
in the mean quantity of RM estimated for the different species,
which ranges from 2.01% to 2.65% of body mass.
RM myoglobin
RM [Mb] data for seven shark species are shown in Table·2.
Similarities between the Kryvi et al. (1981) [Mb] values
10
5
2
Red muscle mass (kg)
lamnids, including the mako TRMM estimates derived from
the original data presented by Carey et al. (1985). Lateral views
of each shark together with one-half transverse sections of the
body between 40% and 50% FL document specific differences
in the lateral and linear position of RM (Fig.·1). In the blue
sharks and leopard sharks, both of which have a more posterior
and lateral RM position, RM is more uniformly distributed
along the body (i.e. the relative cross-sectional area remains at
a near maximal value between 50% and 80% FL), passing
through the caudal peduncle and terminating at the base of the
caudal fin (Fig.·1A,B). By contrast, in the lamnids and the
common thresher shark, RM occurs more anterior in the body
and is also in a more central position (Fig.·1C–E). The salmon
shark has the most anterior RM position (peak RM area at
approximately 40% FL) and the RM terminates far anterior of
the caudal peduncle (at approximately 61% FL; Fig.·1C).
Mako shark RM peaks slightly more posteriorly (at
approximately 45% FL) than in the salmon shark but extends
much further along the body, reaching the caudal peduncle
(approximately 90% FL; Fig.·1D). The thresher shark has a
broader region of peak RM area (45–55% FL) and a small
quantity of RM extends as far as 140% into the upper lobe of
the caudal fin (Fig.1E).
1
8
0.5
.0
±0
5
1.0
18
0.2
M
0.1
M
.0
=0
M
TR
0.05
0.02
0.01
1
2
5
10
20
50
Body mass (kg)
100
200
Fig.·2. Scaling of red muscle (RM) mass in five shark species.
Shaded symbols represent sharks that have a more anterior and
central RM position: salmon shark (squares), shortfin mako (circles;
those with a dot in the middle are estimated from Carey et al., 1985)
and common thresher (triangles). Unshaded symbols represent
sharks that have a more posterior and lateral RM position: blue shark
(squares) and leopard shark (diamonds). Species names are given in
Table·1. The line defines the allometric relationship between RM
mass and body mass for all sharks (r2=0.96, N=30), where TRMM is
total red muscle mass (kg) and M is body mass (kg).
reported for the velvet belly lantern shark (Etmopterus spinax;
family Dalatiidae), small spotted catshark (Scyliorhinus
canicula; family Scyliorhinidae) and blackmouth catshark
(Galeus melanopterus; family Scyliorhinidae) and our
estimates
for
a
single
gray
smoothhound
(7.5·mg·Mb·g–1·tissue) validate our HPLC [Mb] methodology.
On the other hand, our RM [Mb] values for the salmon shark
(mean, 35·mg·Mb·g–1·tissue; range 31–39·mg·Mb·g–1·tissue),
shortfin mako shark (mean ± S.E.M., 21±2.4·mg·Mb·g–1·tissue)
and common thresher shark (16.3±1.6·mg·Mb·g–1·tissue) range
from 3× to 12× higher than values reported by Kryvi et al.
(1981) for sharks in Table·2 and are among the highest reported
to date for any fish species (Dickson, 1996). The slopes of the
scaling equations determined for both the mako and common
thresher shark [Mb] per g RM tissue do not change with body
mass (i.e. slopes are not significantly different from zero).
RM vascularization and ultrastructure
Mako RM vascularization and ultrastructure details are
shown in Figs·3,·4. Table·3 provides additional morphometric
data (based on a mean lo of 2.06·µm) for mako RM and
comparative data for other species. We found little variation in
the RM ultrastructure and vascularization of the two relatively
small (9.7–12·kg) makos studied. We did, however, note some
collapsed capillaries and a few remaining erythrocytes
(Fig.·3B,C) in some of the RM transverse blocks, which
Red muscle characteristics in sharks 2837
Table 2. Myoglobin concentrations in the red muscle (RM)
Species
(common name)
Shark
Lamna ditropis
(salmon shark)
Isurus oxyrinchus
(shortfin mako)
Alopias vulpinus
(common thresher)
Mustelus californicus
(gray smoothound)
Scyliorhinus canicula
(small spotted catshark)
Etmopterus spinax
(velvet belly lantern shark)
Galeus melastomus
(blackmouth catshark)
Tuna
Thunnus albacares
(yellowfin tuna)
Katsuwonus pelamis
(skipjack tuna)
Thunnus orientalis
(Pacific northern bluefin tuna)
RM
position*
Body mass
(kg)
N
[Myoglobin]†
(mg·Mb·g–1·tissue)
AC
91–114
2
35.1 (range, 31.2–38.9)
Present study
AC
6–47
10
21.1±2.4
Present study
AC
6–46
7
16.3±1.6
Present study
PL
0.8
1
7.5
Present study
PL
~0.5‡
3
9.1±1.6
Kryvi et al. (1981)
PL
~0.2‡
3
8.3±0.4
Kryvi et al. (1981)
PL
~0.2‡
3
2.7±0.4
Kryvi et al. (1981)
Source
AC
31.4
Dickson (1996)
AC
20.8
Dickson (1996)
AC
Range, 20–24
Dickson (1996)
*Red muscle position: anterior and central (AC) or posterior and lateral (PL).
†Except where indicated, values represent means ± S.E.M.
‡Sizes given by Kryvi et al. (1981) are ‘adult specimens’, and body mass is estimated from the size at sexual maturation (Froese and Pauly,
2002).
suggests an incomplete in vivo perfusion fixation and thus an
underestimation of QA(0), QA(π/2) and NCAF.
Longitudinal and transverse RM fiber sections (Fig.·3A–C)
detail capillary distributions and suggest the presence of
capillary manifolds. Mako RM capillary density
[QA(0)=743–918·mm–2] appears to be the highest measured to
date for any shark, ranging from 1.7× to 5.9× higher than in
the other species (i.e. the blackmouth catshark and velvet belly
lantern shark) and is also 7× higher than in the Chimaera
monstrosa (rabbit fish) (Table·3). Relative to the other sharks,
RM NCAF is significantly higher in both the shortfin mako
shark and blackmouth catshark, which are not significantly
different from each other. The capillary-to-fiber ratio [NN(c,f)]
is 1.4–10.8× greater in mako RM relative to other sharks and
the rabbit fish (Table·3). Mako shark RM fiber cross-sectional
area [ā(f); 1437·µm2] is not statistically different from the
values for the blackmouth catshark and rabbit fish but is
smaller than in the velvet belly lantern shark (Table·3). An
electron micrograph of mako RM (Fig.·4) shows the
relationship between myofibrils, subsarcolemmal and
intrafibrillar mitochondria and other cellular structures. The
total volume density of mitochondria [VV(mt,f)] in mako RM
(mean, 27.4%) is in the range of values given for the RM of
other sharks (30.4–34.1%) and tunas (28.5%) (Table·3).
Discussion
Our findings support the hypothesis that the lamnid
shark–tuna evolutionary convergence for high-performance
swimming extends to similarities in RM position and in
features augmenting RM aerobic capacity.
RM distribution and scaling
Biomechanical implications of RM position
Aerobically functioning RM powers the sustained
swimming of most fishes. In the majority of sharks and bony
fishes, RM occurs mainly in the posterior half of the body
along the lateral midline, directly under the skin (Greer-Walker
and Pull, 1975; Bone, 1978a; Fig.·1). RM in this position is
linked mechanically to the skin as well as to the adjacent
myotomal white muscle (WM). Force transmission from the
RM to the caudal fin therefore occurs via the skin and also
involves the local bending of body segments remote from the
caudal fin (i.e. the bending waves seen in most fish swimming
modes, including the anguilliform swimming of sharks;
Lindsey, 1978; Sfakiotakis et al., 1999).
In occurring both more anterior in the body and more central
(i.e. nearer the vertebral column; Fig.·1), the lamnid RM
distribution (and that of the common thresher shark) is
different from that of most sharks and similar to that of tunas
(Graham et al., 1983; Carey et al., 1985; Bernal et al., 2001a).
2838 D. Bernal and others
Also, and in contrast to most sharks, lamnid RM is neither
connected to the adjacent WM or the skin. Rather, it extends,
via connective myocomata, directly into the thick skin of the
caudal keel (Reif and Weishampel, 1986; fig. 5 in Bernal et al.,
2001a). Force from the RM is thus transmitted directly to the
A
f
c
c
f
30 µm
caudal fin and does not impose strain on either the surrounding
WM or the adjacent skin.
Similarities in lamnid and tuna RM position have been
postulated to reflect convergence in both body shape and the
development of a more rigid swimming mode. With respect to
body shape, an anterior shift in RM position reduces posteriorbody height, thereby increasing both posterior-body taper and
streamlining (Graham and Dickson, 2000). Biomechanical
studies of skipjack tuna (Katsuwonus pelamis) and yellowfin
tuna (Thunnus albacares) (Shadwick et al., 1999; Katz et al.,
2001; Katz, 2002) and work in progress with the mako shark (J.
Donley and R. Shadwick, personal communication) indicate that
the anterior and central RM position imparts a mechanical
benefit during sustained swimming. This benefit, the reduction
of hydrodynamic drag through a lessening of the extent of lateral
displacement of more anterior body segments during force
production, is derived from the decoupling of RM contraction
from local body bending (this would occur if RM fibers were
connected to either the adjacent WM or skin). In other words,
with a direct link between the remotely positioned RM and the
caudal fin, both tunas and lamnids swim with more rigid bodies,
B
c
f
f
c
f
30 µm
C
mf
f
c
f
im
f
c
f
f
f
f
f
c
f
s
f
sm
f
30 µm
sm
Fig.·3. Light micrographs (400× magnification) of mako shark
(9.7·kg, 95·cm fork length) red muscle (RM) in longitudinal (A,B)
and transverse (C) orientations. The oval in frame A encloses a
putative capillary manifold. Some capillaries (c) and fiber bundles (f)
are labeled for clarity, and arrows point to some remaining
erythrocytes within the capillary lumen.
3 µm
Fig.·4. Electron micrograph (9208× magnification) of a mako shark
(9.7·kg, 95·cm fork length) red muscle (RM) transverse section.
Abbreviations: s, subsarcolemma; mf, myofibrils; im, interfibrillar
mitochondria; sm, subsarcolemmal mitochondria.
Red muscle characteristics in sharks 2839
which reduces induced drag (Shadwick et al., 1999; Altringham
and Shadwick, 2001; Bernal et al., 2001a; Katz, 2002).
anterior RM position of tunas and lamnids is closely linked to
another unique feature shared by these groups, the capacity to
maintain elevated temperatures in RM and other tissues
(regional endothermy; Carey et al., 1971; Bernal et al.,
2001a,b). Endothermy increases total aerobic metabolic
RM position and endothermy
In addition to its biomechanical importance, the central and
Table 3. Red muscle (RM) vascularization and ultrastructure in sharks and tuna
Muscle fiber
Capillary numerical
density (mm–2)
Species
(common name; N)
Mass
(kg)
Fork length
(cm)
FL
Sarcomere
length (µm)
lo
QA(0)
Isurus oxyrinchus
(shortfin mako shark; N=2)
9.7
12.0
95
100
2.04±0.01
2.07±0.01
Mean
Galeus melastomus
(blackmouth catshark; N=7)
Etmopterus spinax
(velvet belly lantern shark; N=7)
Chimaera monstrosa
(rabbit fish; N=6)
Katsuwonus pelamis
(skipjack tuna; N=8)
~2
44
QA(π/2)
Area
(µm2)
ā(f)
Diameter*
(µm)
d̄(f)
918±59
743±67
316±28
–
1396±43
1477±83
42.2
43.4
2.055
831
–
1437
42.8
–
484
–
1778±308
47.6
–
141
–
2617±369
57.7
–
118
–
954±303
34.9
1.78±0.02
2880±171
1615±114
560±30
–
Table 3. Continued
Species
(common name; N)
Isurus oxyrinchus
(shortfin mako shark; N=2)
Mean
Galeus melastomus
(blackmouth catshark; N=7)
Etmopterus spinax
(velvet belly lantern shark; N=7)
Chimaera monstrosa
(rabbit fish; N=6)
Katsuwonus pelamis
(skipjack tuna; N=8)
Capillaries
around fiber
NCAF
Capillary-tofiber ratio
NN(c,f)
Capillary
diameter (µm)
d̄(c)
Anisotropy
coefficient
c(K,0)
Capillary
length
per fiber
volume
(mm–2)
JV(c,f)
3.74±0.07
1.28
9.4±0.5
1.19
1092.4
3.64±0.08
1.10
6.4±0.6
–
–
3.69
1.19
7.9
–
–
27.4†; 21.6‡; 5.7§
56
2.5±0.45
0.86
–
–
–
34.1±1.9†
–
1.4±0.26
0.37
–
–
–
30.4±1.8†
–
0.3±0.16
0.11
–
–
–
5.2±0.9†
–
4.97±0.13
1.59
4.0±0.3
1.44±0.04
4143±242
28.5±1.0a,†;
19.7±0.6a,‡;
8.8±1.1a,§;
24–32b,†
66.1±0.9
Volume
density of
mitochondria
(%)
VV
Volume
density of
myofibrils
(%)
VV(my,f)
25.2±0.8†;
21.0±0.8‡;
4.1±0.9§
29.5±1.2†;
22.2±1.3‡;
7.2±1.9§
59.7±1.5
52.3±1.8
All values are means ± S.E.M.
Abbreviations: FL, fork length; QA(0), transverse orientation; QA(π/2), longitudinal orientation.
Data for G. melastomus, E. spinax and C. monstrosa from Totland et al. (1981).
Data for K. pelamis from aMathieu-Costello et al. (1992) and bMoyes et al. (1992).
*Fiber diameter estimated by 2[(ā(f)/π)0.5]; †values given are VV(mt,f) (total mitochondria); ‡values given are VV(mi,f) (interfibrillar
mitochondria); §values given are VV(ms,f) (subsarcolemmal mitochondria).
2840 D. Bernal and others
biochemical capacity (see Bernal et al., 2003) and power
output of tunas and lamnids and has also contributed to the
adaptive radiation of both groups (Carey and Teal, 1966;
Johnston and Brill, 1984; Dickson, 1995, 1996; Brill, 1996;
Altringham and Block, 1997; Graham and Dickson, 2001). The
functional basis of endothermy in both groups is the capacity
of the RM vascular supply to conserve, by counter-current heat
exchange, metabolic heat generated by the continuous action
of the highly oxidative RM (Carey and Teal, 1966, 1969a,b;
Carey et al., 1971, 1985; Anderson and Goldman, 2001; Bernal
et al., 2001a,b). Although the Alopiidae resemble lamnids in
having a central and anterior RM position (Fig.·1) that is served
by a lateral circulation and a small putative heat exchanger
(Bone and Chubb, 1983; Block and Finnerty, 1994; D. Bernal,
C. Sepulveda and K. Dickson, personal observations), there are
no published descriptions conclusively documenting RM
endothermy in the thresher sharks (Carey et al., 1971).
Interspecific differences in RM position
Although we found the RM position of the two lamnids and
the common thresher shark to be generally similar to that of
tunas, there are noteworthy specific differences among the
sharks (Fig.·1). In makos, RM ends at the caudal peduncle
(approximately 90% FL). In the salmon shark, RM ends well
in advance of the peduncle (approximately 61% FL) and, in
the thresher, RM reaches far into the caudal fin’s upper lobe
(140% FL).
How might these various RM positions relate to the
locomotion and biology of the different species? Assuming the
RM–caudal fin linkage of the salmon shark is similar to that of
the mako, a shorter RM section requires a longer forcetransmitting connection between RM and the caudal fin. This
would in turn imply a more rigid (less undulatory) swimming
mode for the salmon shark relative to the mako. By this
standard, extension of RM well into the upper caudal lobe of
the common thresher’s caudal fin implies greater tail flexibility
(i.e. both maneuverability and mobility), which is consistent
with the tail’s importance in feeding (Gubanov, 1972). During
feeding, we have observed the long caudal lobe of threshers
being used to herd small schooling fishes (e.g. sardines and
anchovies) into a tight group and then ‘clubbing’ and stunning
the prey prior to feeding. Also, many of the thresher sharks we
captured for this study were hooked by the upper lobe of the
caudal tail, a capture scenario also reported by Gruber and
Compagno (1981).
Comparative aspects of RM scaling
Findings for sharks in this study indicate TRMM values of
2–3% of total body mass with no interspecific differences
(Table·1). Thus, neither RM position nor presumed differences
(based on morphology and behavior) in high-performance
swimming capacity (i.e. lamnids vs less mobile forms)
correlate with TRMM.
This contrasts with what is known for tunas, in which
TRMM ranges from 4% to 13% of total body mass (Graham
et al., 1983). While the relative amount of RM in some tuna
species is higher than in any other fish species (e.g. black
skipjack tuna Euthynnus lineatus 11%; frigate tuna Auxis
thazard 13%), the TRMM of most tunas is similar to values
for other fishes (Graham et al., 1983; Graham and Dickson,
2000, 2001). Furthermore, comparisons within the family
Scombridae show that the scaling coefficient for tuna RM is
less than or equal to 1.0, while the RM scaling coefficient for
non-tunas is significantly greater than 1.0 (Graham et al., 1983;
Goolish, 1989). Thus, while tuna TRMM is directly
proportional to body size, or even declines with size in some
tuna species, TRMM in non-tuna scombrids increases at a
disproportionately greater rate than body size.
The RM scaling coefficient determined for lamnids in this
study is not different from that of non-lamnids, and the
combined scaling equation for all sharks examined has a slope
of 1. As reviewed by Webb (1978) and Videler (1993), drag
on a swimming fish is determined mainly by velocity and
wetted surface area. Considering that the wetted surface area
of the shark (i.e. the skin) scales with total body surface area,
the principal effect of body growth on swimming power
requirements are cruising speed (usually a function of FL) and
surface area (M0.67). Therefore, the most conservative
interpretation to make of an RM scaling coefficient of M1 is
that, over the size range of makos examined, mass-proportional
increases in TRMM would be more than adequate to power
cruise swimming. However, we do not know how RM scaling
or the scaling of several morphological features (e.g. body
cross-sectional area, paired-fin lift area, caudal fin area)
affecting drag, lift or the minimum sustainable velocity (i.e. the
minimum velocity required for hydrostatic equilibrium and for
ram gill ventilation) might vary across the entire size range of
the mako [maximum total length, 400·cm (Compagno, 1998);
2001 International Game Fish Association recorded maximum
mass, 554·kg] or that of other species we studied. We therefore
cannot rule out the possibility of a change in RM scaling in
larger makos or other lamnids. Carey et al. (1985), for
example, reported a TRMM of approximately 3% of body
mass for a small (approximately 200·kg) white shark
(Carcharodon carcharias) but a TRMM of 6% of body mass
in a much larger (1256·kg) specimen (Table·1). [Carey et al.
(1985) expressed their TRMM data as a percentage of total
axial muscle mass, which is here converted to percent total
body mass.]
Thus, more RM scaling data and information about the
scaling of factors influencing the biomechanics and physiology
of high performance are needed to determine whether RM
scaling differs in sharks with different RM distribution
patterns. RM scaling differences in tuna and non-tuna
scombrids have been attributed to the positive effect of
temperature on RM function (Graham et al., 1983). Studies of
mako endothermy have also raised the possibility of a
physiological influence on RM scaling based on the finding
that, by having a warmer RM, larger makos achieve a
disproportionately greater power production per unit tissue
mass (Bernal et al., 2001b, 2003).
Red muscle characteristics in sharks 2841
Oxygen delivery to RM
Animals having a high aerobic scope usually also possess
cardiorespiratory adaptations favoring high O2 delivery to the
working tissues. Compared with other fishes, tunas have both
a high metabolic rate and a high O2 transport capacity (Lowe
et al., 2000; Brill and Bushnell, 2001; Korsmeyer and Dewar,
2001). Tuna RM is also relatively specialized for a high O2
flux rate, having small diameter RM fibers with a high [Mb]
and a rich supply of capillaries characterized by structural
modifications (e.g. manifolds) that optimize O2 transfer by
maximizing the fiber–capillary contact area and extending red
cell residence time (Mathieu-Costello et al., 1992, 1995, 1996;
Dickson, 1996).
The mako shark also has numerous morphological and
physiological attributes consistent with a high rate of O2
delivery to its tissues (Bernal et al., 2001a), and initial studies
indicate a high metabolic rate and high tissue aerobic capacity
compared with other sharks (Graham et al., 1990; Dickson et
al., 1993). Our study of the mako has also confirmed
specializations related to a greater RM O2 flux.
RM [Mb]
Myoglobin facilitates the diffusion of O2 from a capillary to
its site of utilization within the mitochondria; a larger [Mb] is
thus indicative of a greater potential for O2 flux (Wittenberg,
1970; Sidell, 1998; Suzuki and Imai, 1998). The finding of a
high RM [Mb] in the mako, salmon and thresher sharks
indicates that RM in all three species is poised for elevated O2
transfer. Moreover, the RM [Mb] of these sharks is much
higher than reported for other sharks (Table·2) and exceeds
values reported for most other fishes except tunas (Dickson,
1996; Table·2). Our data do not show a significant scaling for
RM [Mb] in either the mako or thresher sharks (Table·2) and
we therefore have no new insight concerning the postulated
role of intracellular [Mb] in compensating for size-related
changes in blood circulation time (reviewed in Kayar et al.,
1994; Goolish, 1995).
RM ultrastructure
RM ultrastructure was examined in only two relatively small
(9.7–12·kg) mako sharks. Even though there was little
difference between these sharks, our data are not adequate to
fully describe mako RM ultrastructural properties or to make
definitive comparisons with other species. The finding of
collapsed capillaries and remaining erythrocytes in some of the
RM transverse blocks moreover indicates an incomplete in vivo
perfusion-fixation in some cases, meaning that QA(0), QA(π/2)
and NCAF were probably underestimated. Nevertheless,
because this is the first ultrastructure information reported for
a lamnid shark, a general comparison of mako RM with that
of other species is warranted. Only limited comparisons are
possible because of the paucity of comparative information and
because important details such as specimen body mass and the
sarcomere length (lo) at which fiber data were obtained are
usually not reported. It is critically important to indicate lo
because the state of muscle contraction affects both fiber crosssectional area and fiber diameter estimates (Mathieu-Costello
and Hepple, 2002).
Mako RM fiber cross-sectional areas (at lo=2.06·µm) are
similar to those reported for other sharks (Table·3). However,
mako RM capillary density [QA(0)=831·mm–2] and capillaryto-fiber ratio [NN(c,f)=1.19], which are the highest measured
for any shark species (Table·3), do indicate a greater O2
diffusion capacity. Also, the mako RM capillary orientation
coefficient [c(K,0)=1.19] indicates a 19% increase in capillary
length of contact per volume of muscle fiber
[JV(c,f)=1092·mm–2] than would occur if the capillaries were
straight and unbranched (Mathieu-Costello et al., 1992). While
our data for mako RM ultrastructure identify features related
to an increased O2 flux capacity relative to other sharks,
Table·3 indicates that these vascular specializations are much
less extensive than those in tunas.
Mathieu-Costello et al. (1992) reported the presence of
capillary manifolds in tuna locomotor muscle and suggested
that these facilitated O2 diffusion by increasing the
capillary–fiber contact area. Capillary manifolds, which are
most frequently found at the venular end of the vessel bed, also
occur in the locomotor muscle of active birds (MathieuCostello et al., 1992). Birds and most fishes are similar in
having nucleated erythrocytes and, because these are both
larger and less deformable that non-nucleated erythrocytes, a
possible role for capillary manifolds in enhancing red cell flow
was suggested (Mathieu-Costello et al., 1992).
In view of the proposed role of manifolds in augmenting
circulation, we expected to find large numbers of these
structures in mako RM. In addition, with shark erythrocyte
diameters averaging about 4× higher than those of tunas
(Emery, 1986; Bernal et al., 2001a) and because our study
(Table·3) indicates that mako RM capillary diameter is about
2× larger than in tunas, we predicted that mako manifolds
would be larger.
Capillary manifolds were neither obvious nor abundant in
mako RM. Fig.·3A shows what appears to be a capillary
manifold in a longitudinal RM section, but this structure is
much smaller than tuna manifolds (Mathieu-Costello et al.,
1992), which is inconsistent with the supposed function of
facilitating the flow of larger, less compliant red cells. However,
we studied a limited number of longitudinal RM sections from
which manifolds could be documented, and additional studies
are needed to verify the presence of manifolds in makos and to
search for them in larger specimens, other lamnids and other
active sharks. It could be that differences between tunas and
makos insofar as manifolds are concerned reflect differences in
absolute RM O2 demand; while the metabolic rate of a
swimming mako is higher than that of other sharks, it is about
4× less than that of a tuna (Graham et al., 1990; Bernal et al.,
2001a; Korsmeyer and Dewar, 2001).
Mako RM total mitochondrial volume density is 25–29%,
which is in the range of other sharks and tunas (Table·3). As
reviewed by Mathieu-Costello et al. (1992), conformance in
mitochondrial volume density among most fishes is generally
2842 D. Bernal and others
regarded as indicating the maximum amount of non-contractile
elements that can be contained within the myofibril without
affecting muscle contractility (Block, 1991; Ballantyne, 1995).
In summary, lamnid–tuna evolutionary convergence in
specializations for high-performance swimming extends to
similarities in RM position but not in RM amount, which for
tunas is larger, more variable and scales negatively with body
mass in some species. All sharks in this study had 2–3%
TRMM and, irrespective of RM position, had an RM scaling
coefficient of 1. Similarities in tuna and lamnid RM position
have a basis in similar swimming biomechanics and may also
relate to the presence of regional endothermy. The common
thresher shark has an RM distribution similar to that of the
mako. Tuna and lamnid RM is similar in having specializations
enhancing O2 delivery to the mitochondria, including a high
[Mb], large capillary-to-fiber ratios and structural
modifications increasing capillary–fiber contact, and both
groups have similar myofibrillar mitochondrial densities. Tuna
RM, however, appears to have a greater degree of
‘specializations for O2 delivery’, as evidenced, for example, by
higher capillary density, a more extensive capillary manifold
system and higher capillary tortuosity. Nonetheless, relative to
other sharks, lamnids have many of the adaptations that may
allow for a higher O2 flux to the RM, which can potentially
increase the aerobic capacity of this tissue. Additional studies
comparing the RM morphology, vascularization and
ultrastructure of other actively swimming ectothermic sharks
are needed to understand the degree of lamnid RM
morphological specializations that support their categorization
as high-performance swimmers.
ā(f)
c(K,0)
d̄(c)
d̄(f)
JV(c,f)
K
lo
NCAF
NN(c,f)
QA(0)
QA(π/2)
VV(mt,f)
List of symbols
mean fiber cross-sectional area
capillary orientation coefficient
mean capillary diameter
mean fiber diameter
total capillary length per volume of muscle fiber
capillary anisotropy concentration parameter
sarcomere length
number of capillaries surrounding each
muscle fiber
capillary-to-fiber ratio
capillary density per mm2 transverse sectional
area of muscle fiber
capillary density per mm2 longitudinal sectional
area of muscle fiber
total volume density of mitochondria
We are grateful to Drs K. Dickson, N. Holland, R.
Rosenblatt and R. Shadwick for critically reviewing early
drafts of this manuscript. We also thank two anonymous
reviewers for their suggestions. This study could not have
been possible without the help for specimen collection by the
captain and crew of the Research Vessels David Starr Jordan,
Gordon Sproul, Mako, Yellowfin and Splunky I, the Fishing
Vessels Legend, Sharktagger and Korean Limits and the
logistical support of the kind people at Chesapeake Fish Co.,
Sal Randazzo, Sal Mejia and Nick Vitalich, Jr, and Kent
Williams of New FishHall Bait Company. We are indebted to
C. Brown, E. Banes, G. Bergsma, G. Bernal, C. Brown, C.
Hayleman, R. Hodges, J. Isaacs, A. Jarette, G. Lo, S. Maistro,
S. Miller, C. Parinello, B. Simmons and S. Wagner for
assistance with the data collection on muscle morphology.
Special thanks are due to H. Lee, N. Carter, C. Chan, J.
Donley, H. Dowis, S. Kanatous, C. Li, M. Trejo-Morales and
J. Yan for invaluable help in data collection and analysis and
to J. Valdez for logistical assistance. Support for D.B. was
through the U.C. San Diego Fellowship and an NSF Graduate
Fellowship. C.S. was supported by the Scripps Institution of
Oceanography (SIO Directors Office and the Birch Aquarium
at SIO). This work was partially supported by NSF IBN
9607699, NSF IBN 0077502 and by the University of
California San Diego Academic Senate.
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